#### You may also like ### Getting an Angle

How can you make an angle of 60 degrees by folding a sheet of paper twice? ### Arclets Explained

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website. ### Bow Tie

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

# Integral Polygons

##### Age 11 to 14 ShortChallenge Level
The greatest number of sides the polygon could have is $360$.

As each interior angle of the polygon is a whole number of degrees, the same must apply to each exterior angle. The sum of the exterior angles of a polygon is $360^{\circ}$ and so the greatest number of sides will be that of $360$-sided polygon in which each interior angle is $179^{\circ}$, thus making each exterior angle $1^{\circ}$.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.